Towards Graph-Based Deep Learning for Map Generalization: Insights from Building Footprints Simplification and Aggregation

Map generalization remains one of the fundamental tasks in cartography, especially for the simplification and aggregation of complex building footprints. This study presents the first exploratory application of graph-based deep learning to both tasks, reformulating simplification as node movement prediction and aggregation as link prediction within a unified graph learning framework. We evaluate representative graph neural network architectures (GCN, GAT, and GraphSAGE) on multi-scale building datasets, showing that GraphSAGE demonstrates relative strengths in link prediction accuracy, while also revealing persistent challenges in precise node movement prediction. Beyond quantitative performance, the results highlight that aggregation poses greater complexity and challenges than simplification, underscoring the difficulty of capturing higher-level spatial relationships in map generalization with current deep learning approaches. Although limitations such as data imbalance and the need for post-processing remain, the study provides valuable insights and methodological directions for advancing automated map generalization with deep learning approaches.

Randomized Neural Networks for Integro-Differential Equations with Application to Neutron Transport

Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such nonlocality often introduces dense coupling blocks in deterministic discretizations, leading to increased computational cost and memory usage, while physics-informed neural networks may suffer from expensive nonconvex training and sensitivity to hyperparameter choices. In this work, we present randomized neural networks (RaNNs) as a mesh-free collocation framework for linear integro-differential equations. Because the RaNN approximation is intrinsically dense through globally supported random features, the nonlocal integral operator does not introduce an additional loss of sparsity, while the approximate solution can still be represented with relatively few trainable degrees of freedom. By randomly fixing the hidden-layer parameters and solving only for the linear output weights, the training procedure reduces to a convex least-squares problem in the output coefficients, enabling stable and efficient optimization. As a representative application, we apply the proposed framework to the steady neutron transport equation, a high-dimensional linear integro-differential model featuring scattering integrals and diverse boundary conditions. Extensive numerical experiments demonstrate that, in the reported test settings, the RaNN approach achieves competitive accuracy while incurring substantially lower training cost than the selected neural and deterministic baselines, highlighting RaNNs as a robust and efficient alternative for the numerical simulation of nonlocal linear operators.